Background: In this narrative review, we examine large language models (LLMs) as an emerging component of cardiovascular artificial intelligence and propose the concept of integrative intelligence as a physician-supervised orchestration framework rather than a new model architecture. Current cardiovascular evidence remains heterogeneous and includes text-based LLMs, multimodal foundation or vision-language models, and dedicated modality-specific algorithms for electrocardiography (ECG), echocardiography, computed tomography (CT), cardiovascular magnetic resonance imaging (CMR), and physiological signals. Accordingly, conventional text–based LLMs should not be assumed to interpret raw cardiovascular waveforms or images directly. Instead, their most plausible near-term role is to synthesize clinical text, structured electronic health record data, biomarkers, retrieved evidence, and validated outputs from specialized analytical systems. Methods: We reviewed applications in acute coronary syndromes, heart failure, arrhythmias, valvular disease, cardio-oncology, documentation, and decision support, while distinguishing clinically evaluated applications from proof-of-concept and proposed future uses. Results: Available randomized and prospective evidence is still limited, and reported benefits are task-dependent; improvements in diagnostic reasoning, workflow, or intermediate decision-support measures should not be interpreted as established reductions in major cardiovascular events, readmissions, or mortality. We therefore emphasize data acquisition and multimodal fusion, external and prospective validation, calibration, omission errors, hallucinations, prompt sensitivity, automation bias, model drift, subgroup and out-of-distribution performance, evidence provenance, retrieval-augmented generation failure modes, cybersecurity, regulation, governance, and professional accountability. Conclusion: Integrative intelligence is presented as a testable translational framework for combining specialized AI, multimodal models, evidence retrieval, and human clinical judgment. Its clinical value will depend on rigorous multicenter validation, transparent auditability, and preservation of physician responsibility. Relevance for Patients: This review clarifies the emerging role of LLMs in cardiovascular medicine and proposes a physician-supervised framework for safe multimodal clinical integration.